Analytical solution for longitudinal seismic response of variable stiffness tunnel with isolation layers under shear waves

Abstract

Seismic isolation design typically emphasizes transverse responses of tunnels, with comparatively limited research on longitudinal isolation responses. Previous analytical solutions for isolation response are inapplicable to variable stiffness tunnels. To address research gaps, analytical solutions for longitudinal seismic responses of variable stiffness tunnels with isolation layers are proposed. The solution can be applied to engineering. The mechanical model of isolation layers is developed using the Kelvin model. The variable stiffness tunnel is simplified as two semi-infinite beams embedded in homogeneous and isotropic soil layers. Governing equations are solved using integral transformations and continuity conditions. Analytical expressions are obtained by introducing displacement phase angles to simulate traveling wave effects. The proposed analytical solutions are validated through comparisons with results from existing literature and verified using numerical simulations. Parametric sensitivity analyses are conducted to investigate effects of tunnels with and without an isolation layer, isolation layer thickness and elastic modulus, tunnel stiffness ratio, and wavelength and amplitude of shear waves on seismic responses of variable stiffness tunnels. Changes in stiffness have a more significant effect on internal forces than displacements. Additionally, isolation layer’s thickness and elastic modulus can be optimized through our method to balance structural performance and economic efficiency.

Keywords

isolation layer / variable stiffness tunnel / analytical solution / seismic response / shear waves

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